142 research outputs found
Multipole moments in Kaluza-Klein theories
This paper contains discussion of the problem of motion of extended i.e. non
point test bodies in multidimensional space. Extended bodies are described in
terms of so called multipole moments. Using approximated form of equations of
motion for extended bodies deviation from geodesic motion is derived. Results
are applied to special form of space-time.Comment: 11 pages, AMS-TeX, few misprints corrected, to appear in Classical
and Quantum Gravit
Coframe teleparallel models of gravity. Exact solutions
The superstring and superbrane theories which include gravity as a necessary
and fundamental part renew an interest to alternative representations of
general relativity as well as the alternative models of gravity. We study the
coframe teleparallel theory of gravity with a most general quadratic
Lagrangian. The coframe field on a differentiable manifold is a basic dynamical
variable. A metric tensor as well as a metric compatible connection is
generated by a coframe in a unique manner. The Lagrangian is a general linear
combination of Weitzenb\"{o}ck's quadratic invariants with free dimensionless
parameters \r_1,\r_2,\r_3.
Every independent term of the Lagrangian is a global SO(1,3)-invariant
4-form. For a special choice of parameters which confirms with the local
SO(1,3) invariance this theory gives an alternative description of Einsteinian
gravity - teleparallel equivalent of GR.
We prove that the sign of the scalar curvature of a metric generated by a
static spherical-symmetric solution depends only on a relation between the free
parameters. The scalar curvature vanishes only for a subclass of models with
\r_1=0. This subclass includes the teleparallel equivalent of GR. We obtain
the explicit form of all spherically symmetric static solutions of the
``diagonal'' type to the field equations for an arbitrary choice of free
parameters. We prove that the unique asymptotic-flat solution with Newtonian
limit is the Schwarzschild solution that holds for a subclass of teleparallel
models with \r_1=0. Thus the Yang-Mills-type term of the general quadratic
coframe Lagrangian should be rejected.Comment: 28 pages, Latex error is fixe
General relativistic spinning fluids with a modified projection tensor
An energy-momentum tensor for general relativistic spinning fluids compatible
with Tulczyjew-type supplementary condition is derived from the variation of a
general Lagrangian with unspecified explicit form. This tensor is the sum of a
term containing the Belinfante-Rosenfeld tensor and a modified perfect-fluid
energy-momentum tensor in which the four-velocity is replaced by a unit
four-vector in the direction of fluid momentum. The equations of motion are
obtained and it is shown that they admit a Friedmann-Robertson-Walker
space-time as a solution.Comment: Submitted to General Relativity and Gravitatio
A Generalization of the Goldberg-Sachs Theorem and its Consequences
The Goldberg-Sachs theorem is generalized for all four-dimensional manifolds
endowed with torsion-free connection compatible with the metric, the treatment
includes all signatures as well as complex manifolds. It is shown that when the
Weyl tensor is algebraically special severe geometric restrictions are imposed.
In particular it is demonstrated that the simple self-dual eigenbivectors of
the Weyl tensor generate integrable isotropic planes. Another result obtained
here is that if the self-dual part of the Weyl tensor vanishes in a Ricci-flat
manifold of (2,2) signature the manifold must be Calabi-Yau or symplectic and
admits a solution for the source-free Einstein-Maxwell equations.Comment: 14 pages. This version matches the published on
On a class of invariant coframe operators with application to gravity
Let a differential 4D-manifold with a smooth coframe field be given. Consider
the operators on it that are linear in the second order derivatives or
quadratic in the first order derivatives of the coframe, both with coefficients
that depend on the coframe variables. The paper exhibits the class of operators
that are invariant under a general change of coordinates, and, also, invariant
under the global SO(1,3)-transformation of the coframe. A general class of
field equations is constructed. We display two subclasses in it. The subclass
of field equations that are derivable from action principles by free variations
and the subclass of field equations for which spherical-symmetric solutions,
Minkowskian at infinity exist. Then, for the spherical-symmetric solutions, the
resulting metric is computed. Invoking the Geodesic Postulate, we find all the
equations that are experimentally (by the 3 classical tests) indistinguishable
from Einstein field equations. This family includes, of course, also Einstein
equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool
employed in the paper is an invariant formulation reminiscent of Cartan's
structural equations. The article sheds light on the possibilities and
limitations of the coframe gravity. It may also serve as a general procedure to
derive covariant field equations
Cosmological model with macroscopic spin fluid
We consider a Friedmann-Robertson-Walker cosmological model with some exotic
perfect fluid with spin known as the Weyssenhoff fluid. The possibility that
the dark energy may be described in part by the Weyssenhoff fluid is discussed.
The observational constraint coming from supernovae type Ia observations is
established. This result indicates that, whereas the cosmological constant is
still needed to explain current observations, the model with spin fluid is
admissible. For high redshifts the differences between the model with
spin fluid and the cold dark matter model with a cosmological constant become
detectable observationally for the flat case with .
From the maximum likelihood method we obtain the value of
. This gives us the limit
at the level. While the model with
``brane effects'' is preferred by the supernovae Ia data, the model with spin
fluid is statistically admissible. For comparison, the limit on the spin fluid
coming from cosmic microwave background anisotropies is also obtained. The
uncertainties in the location of a first peak give the interval . From big bang nucleosynthesis we
obtain the strongest limit . The
interconnection between the model considered and brane models is also pointed
out.Comment: RevTeX4, 15 pages, 10 figures; some minor change
Correlation between depression and burden observed in informal caregivers of people suffering from dementia with time spent on caregiving and dementia severity
[Abstract] OBJECTIVE: The aim of the study is to compare data on the examined population of informal caregivers of people suffering from dementia with previous studies, as well as to assess the correlation between (i) depression determined on the basis of the Center for Epidemiologic Studies Depression Scale and (ii) caregiver burden measured by means of the Zarit Caregiver Burden Scale and some chosen parameters, such as total time devoted to caregiving, time of caregiving in hours per week and level of dementia severity measured by Global Deterioration Scale.
PATIENTS AND METHODS: 41 informal caregivers of people suffering from dementia from different backgrounds were evaluated using the Zarit Caregiver Burden Scale and the Center for Epidemiologic Studies Depression Scale. Demographic data about the time devoted to caregiving and the number of hours spend on caregiving weekly were gathered. The type of dementia and its stage were registered using the Global Deterioration Scale (GDS). With the aid of the Statistica StatSoft program, mutual correlations between the parameters were measured. The study was conducted within the framework of AAL UnderstAID – a platform that supports and helps to understand and assist caregivers in the care of a relative with dementia. The international project is co-founded by the Joint Programme Ambient Assisted Living (Grant code: ESR-aal 2012 5 107).
RESULTS: No significant correlations between the level of depression severity evaluated in caregivers and the total time of taking care of a demented person or time of caregiving in hours per week were observed. Similarly, no significant correlation between depression severity level and dementia severity level measured on the GDS scale were noted. There was also no significant correlation between Zarit Caregiver Burden Scale scores and the above-mentioned parameters.
CONCLUSIONS: The level of depression among caregivers do not depend on socio-demographic factors
Eutectic Colony Formation: A Stability Analysis
Experiments have widely shown that a steady-state lamellar eutectic
solidification front is destabilized on a scale much larger than the lamellar
spacing by the rejection of a dilute ternary impurity and forms two-phase cells
commonly referred to as `eutectic colonies'. We extend the stability analysis
of Datye and Langer for a binary eutectic to include the effect of a ternary
impurity. We find that the expressions for the critical onset velocity and
morphological instability wavelength are analogous to those for the classic
Mullins-Sekerka instability of a monophase planar interface, albeit with an
effective surface tension that depends on the geometry of the lamellar
interface and, non-trivially, on interlamellar diffusion. A qualitatively new
aspect of this instability is the occurence of oscillatory modes due to the
interplay between the destabilizing effect of the ternary impurity and the
dynamical feedback of the local change in lamellar spacing on the front motion.
In a transient regime, these modes lead to the formation of large scale
oscillatory microstructures for which there is recent experimental evidence in
a transparent organic system. Moreover, it is shown that the eutectic front
dynamics on a scale larger than the lamellar spacing can be formulated as an
effective monophase interface free boundary problem with a modified
Gibbs-Thomson condition that is coupled to a slow evolution equation for the
lamellar spacing. This formulation provides additional physical insights into
the nature of the instability and a simple means to calculate an approximate
stability spectrum. Finally, we investigate the influence of the ternary
impurity on a short wavelength oscillatory instability that is already present
at off-eutectic compositions in binary eutectics.Comment: 26 pages RevTex, 14 figures (28 EPS files); some minor changes;
references adde
Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid
A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff
fluid in general relativity is performed using the 1+3 covariant approach that
enables the dynamics of the fluid to be determined without assuming any
particular form for the space-time metric. The spin contributions to the field
equations produce a bounce that averts an initial singularity, provided that
the spin density exceeds the rate of shear. At later times, when the spin
contribution can be neglected, a Weyssenhoff fluid reduces to a standard
cosmological fluid in general relativity. Numerical solutions for the time
evolution of the generalised scale factor in spatially-curved models are
presented, some of which exhibit eternal oscillatory behaviour without any
singularities. In spatially-flat models, analytical solutions for particular
values of the equation-of-state parameter are derived. Although the scale
factor of a Weyssenhoff fluid generically has a positive temporal curvature
near a bounce, it requires unreasonable fine tuning of the equation-of-state
parameter to produce a sufficiently extended period of inflation to fit the
current observational data.Comment: 34 pages, 18 figure
Torsion-induced spin precession
We investigate the motion of a spinning test particle in a spatially-flat
FRW-type space-time in the framework of the Einstein-Cartan theory. The
space-time has a torsion arising from a spinning fluid filling the space-time.
We show that for spinning particles with nonzero transverse spin components,
the torsion induces a precession of particle spin around the direction of the
fluid spin. We also show that a charged spinning particle moving in a
torsion-less spatially-flat FRW space-time in the presence of a uniform
magnetic field undergoes a precession of a different character.Comment: latex, 4 eps figure
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